N4palm wrote: Teacher has 100 weights with masses $1$ g, $2$ g, $\dots$, $100$ g. He wants to give 30 weights to Petya and 30 weights to Vasya so that no 11 Petya's weights have the same total mass as some 12 Vasya's weights, and no 11 Vasya's weights have the same total mass as some 12 Petya's weights. Can the teacher do that? Huhh ? $\{1,2,3,...,30\}$ and $\{31,32,...,60\}$ for example ? Or maybe I misunderstood something ....